Question

what is the next term for the sequence: 2.94, 1.94, 0.94, -0.06, -1.06,...

Explanation:

Step1: Identify the common difference

To find the next term in the sequence \(2.94, 1.94, 0.94, -0.06, -1.06, \dots\), we first check the common difference between consecutive terms.
Subtract the first term from the second term: \(1.94 - 2.94 = -1\)
Subtract the second term from the third term: \(0.94 - 1.94 = -1\)
Subtract the third term from the fourth term: \(-0.06 - 0.94 = -1\)
Subtract the fourth term from the fifth term: \(-1.06 - (-0.06) = -1\)
So, the common difference \(d = -1\).

Step2: Calculate the next term

The last given term is \(-1.06\). To find the next term, we add the common difference to the last term:
\(-1.06 + (-1) = -2.06\)

Answer:

\(-2.06\) (corresponding to the option with value \(-2.06\))